Duke has the edge over Rice in biomedical engineering (and the rest of the nation, at that) but Rice's electrical engineering department is phenomenal!
Warning, however: I read in the Insider's Guide that the electrical engineering major at Rice is one of the most intense majors. Rice clearly is superior to Duke in electrical engineering.
I really do think Rice > Duke. Durham is such a ghetto and rundown city full of racial tensions towards Duke; many students don't go off campus because it simply isn't safe, nice, or friendly. With Rice, in Houston, the possibilities are endless. Plus Rice's residential college system simply rocks